Researchers who make predictions from educational data are interested in choosing the best regression model possible. Many criteria have been devised for choosing a full or restricted model, and also for selecting the best subset from an all-possible-subsets regression. The relative practical usefulness of three of the criteria used in selecting a regression model was compared in this study: (a) Mallows' C_p, (b) Amemiya's prediction criterion, and (c) Hagerty and Srinivasan's method involving predictive power. Target correlation matrices with 10,000 cases were simulated so that the matrices had varying degrees of effect sizes. The amount of power for each matrix was calculated after one or two predictors was dropped from the full regression model, for sample sizes ranging from n = 25 to n = 150. Also, the null case, when one predictor was uncorrelated with the other predictors, was considered. In addition, comparisons for regression models selected using C_p and prediction criterion were performed using data from the National Educational Longitudinal Study of 1988.